{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Think Bayes: Chapter 7\n",
    "\n",
    "This notebook presents code and exercises from Think Bayes, second edition.\n",
    "\n",
    "Copyright 2016 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "% matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import math\n",
    "import numpy as np\n",
    "\n",
    "from thinkbayes2 import Pmf, Cdf, Suite, Joint\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Warm-up exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Suppose that goal scoring in hockey is well modeled by a \n",
    "Poisson process, and that the long-run goal-scoring rate of the\n",
    "Boston Bruins against the Vancouver Canucks is 2.9 goals per game.\n",
    "In their next game, what is the probability\n",
    "that the Bruins score exactly 3 goals?  Plot the PMF of `k`, the number\n",
    "of goals they score in a game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  Assuming again that the goal scoring rate is 2.9, what is the probability of scoring a total of 9 goals in three games?  Answer this question two ways:\n",
    "\n",
    "1.  Compute the distribution of goals scored in one game and then add it to itself twice to find the distribution of goals scored in 3 games.\n",
    "\n",
    "2.  Use the Poisson PMF with parameter $\\lambda t$, where $\\lambda$ is the rate in goals per game and $t$ is the duration in games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** Suppose that the long-run goal-scoring rate of the\n",
    "Canucks against the Bruins is 2.6 goals per game.  Plot the distribution\n",
    "of `t`, the time until the Canucks score their first goal.\n",
    "In their next game, what is the probability that the Canucks score\n",
    "during the first period (that is, the first third of the game)?\n",
    "\n",
    "Hint: `thinkbayes2` provides `MakeExponentialPmf` and `EvalExponentialCdf`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** Assuming again that the goal scoring rate is 2.8, what is the probability that the Canucks get shut out (that is, don't score for an entire game)?  Answer this question two ways, using the CDF of the exponential distribution and the PMF of the Poisson distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## The Boston Bruins problem\n",
    "\n",
    "The `Hockey` suite contains hypotheses about the goal scoring rate for one team against the other.  The prior is Gaussian, with mean and variance based on previous games in the league.\n",
    "\n",
    "The Likelihood function takes as data the number of goals scored in a game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from thinkbayes2 import MakeNormalPmf\n",
    "from thinkbayes2 import EvalPoissonPmf\n",
    "\n",
    "class Hockey(Suite):\n",
    "    \"\"\"Represents hypotheses about the scoring rate for a team.\"\"\"\n",
    "\n",
    "    def __init__(self, label=None):\n",
    "        \"\"\"Initializes the Hockey object.\n",
    "\n",
    "        label: string\n",
    "        \"\"\"\n",
    "        mu = 2.8\n",
    "        sigma = 0.3\n",
    "\n",
    "        pmf = MakeNormalPmf(mu, sigma, num_sigmas=4, n=101)\n",
    "        Suite.__init__(self, pmf, label=label)\n",
    "            \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        Evaluates the Poisson PMF for lambda and k.\n",
    "\n",
    "        hypo: goal scoring rate in goals per game\n",
    "        data: goals scored in one game\n",
    "        \"\"\"\n",
    "        lam = hypo\n",
    "        k = data\n",
    "        like = EvalPoissonPmf(k, lam)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can initialize a suite for each team:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "suite1 = Hockey('bruins')\n",
    "suite2 = Hockey('canucks')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the priors look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ALcDT+GYP3uzMEmxMo3bg6Am2HS7wl6+/wFZmPFXXXdAbj9PtdfBECau3Hay+\ngWk2Qr2J/M/AcFXNVNWLgeHAX8IXljH1I7i7KyUxmt5pya7GEwk6JMXTPTkwB9r7QfOjmeYt1ISS\nq6qbg8pb8U0QaUyj9uXqff7tYb07uBhJZAmeB23BRuv2Mj413eV1nYhcBywVkZkicrOI/ASYgW+e\nLmMarYM5+Ww9fNJftrm76s8NF/Z2RvXA/rxi1u+yW4hNzWcoVzmPWGA/cDGQCRwEbN5v06i9P28j\nXqe/q0OrFmR0be9uQBGkY9tWdEsOrHT53lfW7WVqHth4S0MFYkx9m70q0N11nnV31bvhZ3Zm6xzf\nJJELNtiFeRP6XV6xInKXiPxDRF4pe4Q7OGPqKievgM0H8/3l687v4WI0kWnsBb383V57jxexZe9R\nV+Mx7gv1ovwbQAq+FRzn4FsEyy7Km0brvXkbKXW6u5Ljo2zwXRic1j6R09u29JfftW6vZi/UhNJT\nVR8GTjjze10BDAlfWMacms9XBhaAGtrTrp2Ey0X9UvzbX62zaViau1ATSrHz7zERORNIAmzIsWmU\ncvIK2HgguLvLBjOGyw8u7oM4I3325hRat1czF2pCeUFE2gIP41t+dy2+VRONaXSCu7vaxUdxTu+U\n6huYOkvtkEhaW9/dXopYt1czF1JCUdWXVPWoqs5R1e6q2rHiqovGNBbB3V3nWXdX2F1s3V7GEepd\nXski8jdnXfdlIvJXEbE5LEyjY91dDc+6vUyZULu83gIOAGOB64FDwNvhCsqYurLuroZn3V6mTKgJ\npbOq/p+qbnMejwJ2H6ZpdKy7yx3DM6zby4SeUGaJyDgR8TiPG4FPwxmYMbVVsbtrrE1V32BuuCjQ\n7bUnxwY5Nlc1TQ6ZKyLHgZ8BU4Ei5/EWcHv4wzMmdBW7uwb1su6uhhLc7QU2yLG5qmnFxkRVbe38\n61HVFs7Do6qtQ/kBIjJKRNaLyEYRub+KOk+LyCYRWSkiA4P2vywi+0VkVYX6j4jIbucmgeUiMiqU\nWExks+4udwV3e81da91ezVGoXV6IyNUi8oTzuDLENh58KzyOBDKA8SLSt0Kd0UAPVe0F3AE8G/T0\nq07byjypqoOcxyehvg4TmQ7nnPSvcw7W3eUGX7eXz97jRWy0Ke2bnVBvG/4jcC++AY1rgXtF5A8h\nNB0MbFLVHapajK+rbEyFOmOA1wFUdRGQJCKdnPI8fOvYVxpWKLGb5uHdrzaUm6reursaXmqHRLq2\nC3R7vT0TbBQdAAAePklEQVTXur2am1DPUC4HLlPVV1T1FWAUvvm8atIF2BVU3u3sq67OnkrqVGai\n00X2kogkhVDfRLDPvtnr37aVGd0z4uzASo5frT/gYiTGDdWuh1JBG+CIs+32H/B/AL9VVRWRR4En\ngZ9WVnHSpEn+7czMTDIzMxsiPtOAso/ksfVQYGXG8cP7uBhN8/aDzL68MmcbXoUDecWs3naQs7pZ\ngm/ssrKyyMrKOuXjhJpQ/gCsEJEv8XU1XQQ8EEK7PcDpQeVUZ1/FOmk11ClHVYNX83kR35LElQpO\nKCYyvT1ng3PDKqQkRtM3zSZxcEuHpHh6doj33779ztyNllCagIpftidPnlyn49TY5SUiAswDhgLv\nA9OA81Q1lJHyS4CeIpIuIjHAOHyTSwabDkxwftZQ4JiqBt8iIlS4XiIiwR3k1wHfhhCLiVCzVwdW\nZry4n423ddv3+wd6rOdvtJUcm5MaE4qqKjBTVfep6nTnkR3KwVW1FJgIzALWAG+p6joRuUNEbnfq\nzAS2ichm4Hng52XtRWQqsADoLSI7RaRsSeLHRWSViKzEt879L0N+xSai7Nifw86jBQAIyrhM6+5y\n2w0X9SbK+Qp4JL+URev2Vd/ARIxQu7yWi8i5qrqktj/AuaW3T4V9z1coT6yi7Q+r2D+htnGYyPTW\nnA2ocwKb2iaWbiltXI7IJCXE0ielFWv3nQDg/fmbGHJG5xpamUgQ6l1eQ4CFIrLFOTNYXXGwoTFu\nmLMm0Dt6yZl2q3BjMWpg4LLows2H8Xq9LkZjGkqoCWUk0B24BLgKuNL51xjXrNtxiL3HiwDfRbYb\nLrLursbiugt6Ee38dckp9DJn1a7qG5iIUNNcXrEi8gvgf/CNPdnjDFLcoao7GiRCY6owNWuDf7tH\n+zhSOyS6GI0JlhAXw1mpgdmZ3pu/xcVoTEOp6QxlCvA9YDUwGvhz2CMyJgRer5d56wN3EI0amOpi\nNKYyY4Z09W8v236MgsJi94IxDaKmhNJPVW9yLqJfD1zYADEZU6MFa/ZwtKAUgBbiu7PINC5XDO5O\nfLTvhomCEmXGoq0uR2TCraaE4v9KoaolYY7FmJC9O2+zfzujSwJJCbHV1DZuaNEiisHd2/nLMxZv\ndy8Y0yBqSij9ReS488gFzi7bdtZJMabBlZSUsmRbYM7Qqwd3czEaU50bgmZ9XrM3j5y8AhejMeFW\n03ooUc56KGVrorQI2g5pPRRj6tu/F20lv9g32UpcC+GqoT1cjshU5bx+p9E2LgqAUoW35qx3OSIT\nTiGvh2JMY/HRou3+7XO6tSUmOsq9YEy1PB4PF/bt6C9/uqLaafpME2cJxTQpufmFfLsn0Nt6wzA7\nO2nsfhg0+/O2wwXsOpDjYjQmnCyhmCZl6pfrKHYGXbeJ9XDh2Xa7cGPXNy2Z1DYxACgw5fN17gZk\nwsYSimlSZi7b7d++6IxOeDz2EW4KRgbNQDx7TbZNxRKh7LfRNBnrdx0uN7PwhBFnuByRCdVNI84o\nNwPxgjV2LSUSWUIxTcY/v1jvn1m4W3IcPbu0dTkiE6q2iXGc2SXBX546x9abj0SWUEyT4PV6y61R\nfvmgtGpqm8bo+qAbKJZtP0p+gU3FEmksoZgm4dOl28kp9PW7x3hg3PC+LkdkauuKId1JjPH9ySks\nhXfnbqihhWlqLKGYJiF4ttoBpyeREBfjYjSmLjweD8N6t/eXZyzZ6WI0JhwsoZhGLyevgG92Bcae\n/OCiXi5GY07FTZcEziy3HDrJjv02JiWSWEIxjd4/Z6+jxDfTCm1joxje366fNFVndetQbkzKK5+u\ncTcgU68soZhG79/LAqv9Dc+wsSdN3eigtWuy1u63MSkRxH4zTaO2aN1e9h333Q3kEbh15JkuR2RO\n1YRL+xETtDzwx7ZOSsSwhGIatddnB2anPSOllS3zGwES41tybvfAGKK3vtpcTW3TlFhCMY1Wbn4h\nS7YG1j0Zd2HPamqbpmRC0MX5ddkn2H0w18VoTH0Je0IRkVEisl5ENorI/VXUeVpENonIShEZGLT/\nZRHZLyKrKtRvKyKzRGSDiHwqIknhfh2m4f3zi7UUOd3rSS09XDGku7sBmXoz5IzT6Nw6GgCvwiuf\nfutyRKY+hDWhiIgHeAYYCWQA40Wkb4U6o4EeqtoLuAN4NujpV522FT0AfK6qfYDZwK/DEL5x2Yyl\ngYkgL7GL8RHnynMCd+t98a1NGBkJwv0bOhjYpKo7VLUYeAsYU6HOGOB1AFVdBCSJSCenPA84yneN\nAaY421OAa8IQu3HRkg372Hu8CPBdjP/pqLNcjsjUN7s4H3nCnVC6ALuCyrudfdXV2VNJnYo6qup+\nAFXNBjrWUN80Ma9+Flgzo69djI9IifEtOadrG3956ly7ON/UtXA7gHqiVT0xadIk/3ZmZiaZmZkN\nEI45FYdzTrI46GL8eLsYH7FuvrQfX7+wAID12SfYvOeozSLtgqysLLKysk75OOFOKHuA04PKqc6+\ninXSaqhT0X4R6aSq+0UkBThQVcXghGKahhc/We0fGd8uLsouxkewIWd0Jq1NS3YdK0SB52eu5k8/\nu8jtsJqdil+2J0+eXKfjhLvLawnQU0TSRSQGGAdMr1BnOjABQESGAsfKurMc4jwqtrnZ2f4J8FE9\nx21c4vV6+c/KwPeJKwal2sX4CHfDsG7+7bkbDpF3ssjFaMypCOtvqqqWAhOBWcAa4C1VXScid4jI\n7U6dmcA2EdkMPA/8vKy9iEwFFgC9RWSniNziPPUYcJmIbABGAH8M5+swDWfavE3kFASmqb9tlI2M\nj3TjMvuS4J/WXpnymc3v1VSJapWXH5o8EdFIfn2R6LpHP2brYd8yvxf3bsdTdw53OSLTEB55fQEf\nrdgHQIdWLfj0t1fZmamLRARVrdgzVCP7HzONxsot+/3JRFBuH223CjcXd155tn/N+YMnSvh8+Q53\nAzJ1YgnFNBovfhLo6ujRPp6Mru2rqW0iSUq7BAaktfaXX5ttqzk2RZZQTKOQfSSPhVsCtwr/8GK7\nVbi5uW1kP//2un15rNtxyMVoTF1YQjGNwt8+Wkmpc7krOT6Ka4ZZQmluzuvXha7tYgFQhKenf+Ny\nRKa2LKEY1+WdLOLzNYGhRDec19UuyDZTN1/S27+9eNsxm4W4ibHfWuO65/69ikLn9CQhxsPNl2W4\nHJFxy9Xn9aBDK99461KFZ2asdDkiUxuWUIyrSkpKmR60xO8VA08jtmW0ixEZN3k8Hn4QNNDxy7UH\nyMkrcDEiUxuWUIyrXv9iLccLnYGMUcLPr+zvckTGbRMuyyDRP9ARnv14VQ0tTGNhCcW4xuv18uZX\ngSnLh/dtT1JCrIsRmcYgJjqKK88JTDj+8fI9FBQWuxiRCZUlFOOat+ds4OCJEgCiBO4eM7CGFqa5\n+PmV/WnpjHTMLfLy/Ew7S2kKLKEYV3i9Xl75YqO/fH7PdrbmifFLjG/JqLNT/OX3Fu60s5QmwBKK\nccWbWevLnZ3cN3aQyxGZxuZX1w0qd5by7L9tXEpjZwnFNDiv18trszf5yxf0akd6pyQXIzKNUVJC\nLJf3D5ylTFu8y85SGjlLKKbBTZ1d/uzkv+3sxFThF9cGzlLy7Cyl0bOEYhqU1+vltS8DZycX9k4m\nraOdnZjKJSXEcsWAzv7ye4t2kl9gZymNlSUU06Be/s9qDuUHn52c43JEprG795qBxLbwnaWcKFb+\n+sFylyMyVbGEYhpM3skipswNGndyRge7s8vUKCkhljFB41I+XLaH7CN5LkZkqmIJxTSYP7+3lLwi\n36j42BbCr2881+WITFPxy2sHkdTS9+eqqFT5w9tLXI7IVMYSimkQew/l8u+V+/zl6wefTnJSnIsR\nmaYktmU0t17Sy1/+atMR1my39VIaG0sopkH87u0lFPtOTmgT62Hi1TZnl6mdH1/aj9NaxwDgVfjd\nO0tdjshUZAnFhN3KLftZsDmwGuPPLutjMwqbWvN4PNx3zdn+8tp9J5i1dJuLEZmKLKGYsPJ6vTzy\nryU4izGS2iaG8Zl9XY3JNF0jBqbTr3Mrf/nxD1ZRVFzqYkQmmCUUE1Yv/2c1O44WAiAovx470FZj\nNKfkN+PPxRnryKH8Ep54z7q+Gouw/2aLyCgRWS8iG0Xk/irqPC0im0RkpYgMqKmtiDwiIrtFZLnz\nGBXu12Fq72BOPq9kbfGXL+yVzPlnproYkYkEfdOSuTJosOP7S3azec/RalqYhhLWhCIiHuAZYCSQ\nAYwXkb4V6owGeqhqL+AO4LkQ2z6pqoOcxyfhfB2mbh6e8jUnS3ydXfHRwuQfD3U5IhMpfv2Dc2kb\nFwVAicLD/1zkckQGwn+GMhjYpKo7VLUYeAsYU6HOGOB1AFVdBCSJSKcQ2kqYYzenYM7KnSzaFvjW\nePulvWibaLcJm/oR2zKa/xlzlr+8LvsE787d4GJEBsKfULoAu4LKu519odSpqe1Ep4vsJRGxyaAa\nkbyTRUx6Zznq5PzuybFMuDTD5ahMpLl8SA8GpAZmWvjrv9dw4OgJFyMyLdwOoBKhnHn8A/itqqqI\nPAo8Cfy0soqTJk3yb2dmZpKZmVkPIZrqPPTafI6e9N1500Lg/24aYhfiTVg8OuE8xj72GYWlyoli\n5X9emceU+0a6HVaTk5WVRVZW1ikfJ9wJZQ9welA51dlXsU5aJXViqmqrqgeD9r8IzKgqgOCEYsLv\n3ws3M3fjYcq+F/zo/HQyurZ3NygTsVI7JHLXyD48OXM9AN/szuO1Wau5+ftn1dDSBKv4ZXvy5Ml1\nOk64vzYuAXqKSLqIxADjgOkV6kwHJgCIyFDgmKrur66tiKQEtb8O+Da8L8OE4nDOSR77YHW5rq57\nr7W1Tkx4Tbgso1zX17OzNrJjf46LETVfYU0oqloKTARmAWuAt1R1nYjcISK3O3VmAttEZDPwPPDz\n6to6h35cRFaJyErgYuCX4XwdpmZer5dfvTSXXGfyx5go4U+3DrOuLtMg/nTbBbSK9n2RKSyFX744\nD6/X63JUzY+oas21migR0Uh+fY3JX6YtZcq8Hf7yxMt6cdvlZ1fTwpj69dGCTTzy7ip/+cr+KTx6\n8/kuRtR0iQiqWus7ae3rozllc1bu5I35gWQyIDXRkolpcGOG9eKSvoHrdR9/s4/35210MaLmxxKK\nOSXZR/L43zeX4XVOBJPjo/jbnRe7G5Rptv546wWktvHNSKwIj324mo27DrscVfNhCcXUWUFhMXf+\nfU7guokH/nrb+STGt3Q5MtNcxURH8ff/uoj4oOspd78wn9z8Qpcjax4soZg68Xq93PWPLLYdKfDv\nu/eKMzirWwcXozIG0jslMenGgf4BbfvzivnpU7MpKbFZicPNEoqpk4enLGDZzuP+8sgzO/KjS/q5\nGJExAd//Xjd+NCzdX954IJ+7n82yO7/CzBKKqbW/T1/Bx6v2+8sDUhP5wy12N41pXP77hu+R2SfZ\nX/566zEenWqTSIaTJRRTK698upqXvtzqL3dtF8tzE4fbeBPTKD15+0VkBC3I9f6yvfzZ1k8JG/sr\nYEL2yqer+dsnG/2rLybHR/HyPZfYcr6m0fJ4PLx4zwj/nV8Ab8zfwRPvWlIJB0soJiQvzVxVLpm0\njY3ipbszSU6yKelN4xYfG82rvxhBSmLgi88/F+zgsXcWuxhVZLKR8qZGT7y7lH8t2O6fo6ttXBSv\n3Tuc9E62aoBpOg7m5PPjP39Odm6xf98VZ3fi/35iUwRVVNeR8pZQTJVKSkq578W5zNl4xL+vXVwU\nU34xnLSOlkxM03M45yQ3PfkZ+44HksrAtNY8e1emdd0GsYRSCUsodZeTV8Adz3zJ+v35/n2dEqJ5\n+Z7hpHZIrKalMY3b0dyT3PyXL9hxNDDYMa1NS168O5OUdgkuRtZ4WEKphCWUulm0bi8PvLHYv0gW\nQN9O8bx4zyU2Ct5EhILCYu76R1a5sVQJMR5+c8MAvv+9bi5G1jhYQqmEJZTa8Xq9PPXBcv45fwel\nQW9bZp9knrjtQlq0iHIvOGPqmdfrZfI/F/LRin3+fQJcPbAzj9w0tFlfV7GEUglLKKHbvOcov57y\nNZsOnvTvixK4NbM7d1090MXIjAmvf81ey1Mz11MU9C0qtU0Mj940mAE9OrkYmXssoVTCEkrNSkpK\n+dN7S5m2eDclQW9VcnwUj/9kKOf0Tqm6sTERYuOuw/zipQXsPV7k3+cRGH1WJx4aP4T42OZ1wd4S\nSiUsoVTN6/Uybd4mnv90PYfyS8o9d173NvzptgtJiIuporUxkaegsJiHX/+az9ceJPivRlKsh59k\n9uTmyzKaTTeYJZRKWEKp3Kyl23j642/Zfayo3P62cVE8cO3ZjDy3u0uRGeO++d/u5rdvL2d/XnG5\n/R0TovmvkX25ZljPiE8sllAqYQkloKSklH/NXsfb87eVO60H37WS0Wen8L/jB9u9+Mbg+315Ytoy\n3l+8i6IKExR3aNWCsUPTufmyjIj9fbGEUglLKLB+12He+Hwdc9cf9C+EVUaAId3acP+N59AtpY07\nARrTiGUfyeOxd5cyd8Phcnc+AsRHC8N6teemS/pE3MV7SyiVaK4JZfOeo3ywYDNz1+5n17HvrlTn\nEeif2ppfXTvAFsQyJgSb9xzliWnLWbL92HcSC0BKYjQX9O3ImPN6RMTvlCWUSjSXhJKbX8gXK3Yy\nb+0+Vu08xoEKfb9lYqKEi/q0566rzrYzEmPqIPtIHs9M/4Yv1uznZEnlf1vaxUdxdlobhvVN4bJz\n0mmb2PQmUG20CUVERgF/xTez8cuq+lgldZ4GRgMngJtVdWV1bUWkLfA2kA5sB25U1ZxKjhtxCaWg\nsJjV2w+xbNN+Vu84wpb9eRzIK8ZbxcsUlG7JcVzxvTR+cHFfu3PLmHpQUFjMtPmbmL5oBxsP5FPV\nXxkBOiRE061DK848vS3f692J/t07NvrbkBtlQhERD7ARGAHsBZYA41R1fVCd0cBEVb1CRIYAT6nq\n0OraishjwGFVfVxE7gfaquoDlfz8JplQcvIK2LY/h10HctmancPOg3nsPXqS/TkFHD1ZWuWHt4wA\n6e1iOb9vR66/sBfdUtqQlZVFZmZmA0Tf+Nl7EWDvRUBd34vdB3P5YP4m5qzJZuvhk1V+uSsj+G5F\nTkmKJaVNHGntE+jROYnTOybSo3MbkhJi6xR/faprQmkRjmCCDAY2qeoOABF5CxgDrA+qMwZ4HUBV\nF4lIkoh0ArpV03YMcLHTfgqQBXwnoTQ0r9dLUXEpJ4tKOFFQQkFRCcfzC8kvKCb3ZDG5+UXkFhSR\nm1/M8fwijp/0/ZtXWMLxk8WcKCjlRFHpd+4qCUXbuCj6dk5kaJ9OXD6kOx2S4ss9b384Auy9CLD3\nIqCu70Vqh0TuvmYQd1/j+zI4c8k2vl6Xzdo9x78zxgtAgWMFXo4V5PsmX91wuNzz0R5oFeOhVcsW\ntI5tQWJcNIlx0STERtOmVQyJcTEkxMfQOi6ahLgYWsX6no+PjaFVbAviYloQEx3lyq3N4U4oXYBd\nQeXd+JJMTXW61NC2k6ruB1DVbBHpeKqBrttxiPte+RpFUcX38B0frwb2eVXxVvJvqfrqlq0ZEk4J\nMR5SWrekV+fWDOzenmEZXWwGYGMagaSEWMYPP4Pxw88A4MDREyxYu5dlmw+wYe9xsnMKyC0srfbv\nRLG3LOEUsSenqMp6NfGIb0iAR8AjUu5fEd9ZSNk+EUEo21/nHxn2hFIXdXk5p9yvlV9Y8p3xGbVX\nP8nEI9Aq2kNibAs6tI6hc9t4unZMpFeXtgzq2bFJXuQzpjnq2LYV15zfi2vO7+Xfl5NXwMrNB9i4\n5yjbD+Sy9+hJDuYWkHuyhNwib41dZqHyfeEtK2mFf8NEVcP2AIYCnwSVHwDur1DnOeAHQeX1QKfq\n2gLr8J2lAKQA66r4+WoPe9jDHvao/aMuf/PDfYayBOgpIunAPmAcML5CnenAXcDbIjIUOKaq+0Xk\nUDVtpwM3A48BPwE+quyH1+WikjHGmLoJa0JR1VIRmQjMInDr7zoRucP3tL6gqjNF5HIR2YzvtuFb\nqmvrHPox4B0RuRXYAdwYztdhjDGmZhE9sNEYY0zDafJTZorIyyKyX0RWVfH8xSJyTESWO4//begY\nG4qIpIrIbBFZIyKrReSeKuo9LSKbRGSliAxo6DgbQijvRXP5bIhISxFZJCIrnPfikSrqNYfPRY3v\nRXP5XIBvrKDzGqdX8XytPhON8S6v2noV+BvOWJYqzFXVqxsoHjeVAL9S1ZUikgAsE5FZlQwk7aGq\nvZyBpM/huwEi0tT4Xjgi/rOhqoUiMlxV80UkCpgvIv9R1cVldZrL5yKU98IR8Z8Lx73AWqB1xSfq\n8plo8mcoqjoPOFpDtWZxcV5Vs8umrVHVPHx3w3WpUK3cQFKgbCBpRAnxvYDm89nIdzZb4vsiWbGv\nu1l8LiCk9wKawedCRFKBy4GXqqhS689Ek08oITrPOWX7WET6uR1MQxCRrsAAYFGFpyoOGN1D5X9o\nI0Y17wU0k8+G07WxAsgGPlPVJRWqNJvPRQjvBTSPz8VfgP+h8oQKdfhMNIeEsgw4XVUHAM8AH7oc\nT9g5XTzvAfc6386brRrei2bz2VBVr6oOBFKBIRH8R7JGIbwXEf+5EJErgP3OWbxQT2dkEZ9QVDWv\n7BRXVf8DRItIO5fDChsRaYHvD+gbqlrZ+Jw9QFpQOdXZF3Fqei+a22cDQFWPA18Coyo81Ww+F2Wq\nei+ayefifOBqEdkKvAkMF5GK16Fr/ZmIlIRSZYYN7vMTkcH4bpU+0lCBueAVYK2qPlXF89OBCQDB\nA0kbKrgGVu170Vw+GyLSXkSSnO044DLKT9AKzeRzEcp70Rw+F6r6oKqerqrd8Q0an62qEypUq/Vn\nosnf5SUiU4FMIFlEdgKPADE4AyeB60XkTqAYOAn8wK1Yw01Ezgd+BKx2+ogVeBDfujHVDiSNNKG8\nFzSfz0ZnYIr4loTwAG87n4MaBxhHoBrfC5rP5+I7TvUzYQMbjTHG1ItI6fIyxhjjMksoxhhj6oUl\nFGOMMfXCEooxxph6YQnFGGNMvbCEYowxpl5YQjERTUQ6isi/RGSziCwRkfkiMqaOx0oXkdX1HaMx\nkcISiol0HwJZqtpTVc/FNyo49RSO1yADt5yp1Y1pUiyhmIglIpcAhar6Ytk+Vd2lqn93nm8pIq+I\nyCoRWSYimc7+dBGZKyJLncd31oAQkX7OQk3LnVlpe1RSJ1dEnhSRb0XkMxFJdvZ3F5H/OGdMc0Sk\nt7P/VRF5VkQW4lvmOvhYcSLytnOs90VkoYgMcp77h4gslgoLRonINhH5vfgWk1osIgNF5BPxLZh0\nR1C9/3aeXylVLL5lTCia/NQrxlQjA1hezfN3AV5VPVtE+gCzRKQXsB+4VFWLRKQnvsnzzq3Q9r+A\nv6rqm84klJWdUbQCFqvqr0TkYXzTAt0DvADcoapbnLmingVGOG26qGplixj9HDiiqmeKSAawIui5\nB1X1mDOdyBciMk1Vv3We266qA0XkSXyL0Q0D4oFvgedF5DKgl6oOFhEBpovIBc46Q8bUiiUU02yI\nyDPABfjOWoY4208DqOoGEdkO9AZ2As+Ib8nTUqBXJYf7GnhIfIsUfaCqmyupUwq842z/E5gmIq3w\n/VF/1/kDDhAd1ObdKsK/APirE+saKb/k9TgR+Rm+3+cUoB++hAEww/l3NdDKmUU3X0QKRKQ18H3g\nMhFZjm+C1VbO67WEYmrNEoqJZGuAsWUFVZ3odDtVtqASBGas/iWQ7Zy5ROGbILAc58xkIXAlMFNE\nblfVrBriUXzdzEdVdVAVdU7UcIxysYpv8bD7gHNU9biIvArEBtUrdP71Bm2XlVs4x/lDcLegMXVl\n11BMxFLV2UDL4OsF+L6Bl/kK34zEONcx0oANQBKwz6kzgUq6s0Skm6puU9W/AR8BZ1cSQhRwvbP9\nI2CequYC20SkbD8iUlnbiubjzHorvgWhznT2twbygFxn2vXRIRwLAsnzU+BW58wJETlNRDqEeAxj\nyrGEYiLdNUCmiGxxziheBe53nvsHEOV0H70J/ERVi539NzvT3vem8rOGG50L5CvwXaupuDgRTrvB\nzq3GmcBvnf0/An7qXAT/Frja2V/dHWT/ANo79X+L7+wrR1VXASuBdfi61YK7qqo7ngKo6mfAVOBr\n5314F0iopp0xVbLp640JExHJVdXEejqWB4hW1UIR6Q58BvRR1ZL6OL4x9cGuoRgTPvX5bS0e+FJE\nyi7g32nJxDQ2doZijDGmXtg1FGOMMfXCEooxxph6YQnFGGNMvbCEYowxpl5YQjHGGFMvLKEYY4yp\nF/8frHUZDbM7+B4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f009a60d210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=2)\n",
    "thinkplot.Pdf(suite1)\n",
    "thinkplot.Pdf(suite2)\n",
    "thinkplot.Config(xlabel='Goals per game',\n",
    "                ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can update each suite with the scores from the first 4 games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.8814477910015515, 2.6145205761109502)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4iCDSLS4G2dPT59adcSL5T/qZHmv0SAHo6VMUVjQPs8J7hIcFkz3b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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f009a5f8f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suite1.UpdateSet([0, 2, 8, 4])\n",
    "suite2.UpdateSet([1, 3, 1, 0])\n",
    "\n",
    "thinkplot.PrePlot(num=2)\n",
    "thinkplot.Pdf(suite1)\n",
    "thinkplot.Pdf(suite2)\n",
    "thinkplot.Config(xlabel='Goals per game',\n",
    "                ylabel='Probability')\n",
    "\n",
    "suite1.Mean(), suite2.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To predict the number of goals scored in the next game we can compute, for each hypothetical value of $\\lambda$, a Poisson distribution of goals scored, then make a weighted mixture of Poissons:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from thinkbayes2 import MakeMixture\n",
    "from thinkbayes2 import MakePoissonPmf\n",
    "\n",
    "def MakeGoalPmf(suite, high=10):\n",
    "    \"\"\"Makes the distribution of goals scored, given distribution of lam.\n",
    "\n",
    "    suite: distribution of goal-scoring rate\n",
    "    high: upper bound\n",
    "\n",
    "    returns: Pmf of goals per game\n",
    "    \"\"\"\n",
    "    metapmf = Pmf()\n",
    "\n",
    "    for lam, prob in suite.Items():\n",
    "        pmf = MakePoissonPmf(lam, high)\n",
    "        metapmf.Set(pmf, prob)\n",
    "\n",
    "    mix = MakeMixture(metapmf, label=suite.label)\n",
    "    return mix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the results look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.8792178420902261, 2.6134252104851328)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Xkr4ArAXOKF+EHecBbmZmluCuJDMzS3BiMDOzBCcGMzNLcGIwM7MEJwYzM0tw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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0097906550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "goal_dist1 = MakeGoalPmf(suite1)\n",
    "goal_dist2 = MakeGoalPmf(suite2)\n",
    "\n",
    "thinkplot.PrePlot(num=2)\n",
    "thinkplot.Pmf(goal_dist1)\n",
    "thinkplot.Pmf(goal_dist2)\n",
    "thinkplot.Config(xlabel='Goals',\n",
    "                ylabel='Probability',\n",
    "                xlim=[-0.7, 11.5])\n",
    "\n",
    "goal_dist1.Mean(), goal_dist2.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the probability that the Bruins win, lose, or tie in regulation time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prob win, loss, tie: 0.457999782312 0.370290326041 0.171709891647\n"
     ]
    }
   ],
   "source": [
    "diff = goal_dist1 - goal_dist2\n",
    "p_win = diff.ProbGreater(0)\n",
    "p_loss = diff.ProbLess(0)\n",
    "p_tie = diff.Prob(0)\n",
    "\n",
    "print('Prob win, loss, tie:', p_win, p_loss, p_tie)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the game goes into overtime, we have to compute the distribution of `t`, the time until the first goal, for each team.  For each hypothetical value of $\\lambda$, the distribution of `t` is exponential, so the predictive distribution is a mixture of exponentials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from thinkbayes2 import MakeExponentialPmf\n",
    "\n",
    "def MakeGoalTimePmf(suite):\n",
    "    \"\"\"Makes the distribution of time til first goal.\n",
    "\n",
    "    suite: distribution of goal-scoring rate\n",
    "\n",
    "    returns: Pmf of goals per game\n",
    "    \"\"\"\n",
    "    metapmf = Pmf()\n",
    "\n",
    "    for lam, prob in suite.Items():\n",
    "        pmf = MakeExponentialPmf(lam, high=2.5, n=1001)\n",
    "        metapmf.Set(pmf, prob)\n",
    "\n",
    "    mix = MakeMixture(metapmf, label=suite.label)\n",
    "    return mix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the predictive distributions for `t` look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.34678105634353618, 0.38140698509499399)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p/35gSXLfRu82qDSfN40eHC3XKpdHnpqfwoicc5koqQnFzBqBqcBsYDEww8yW\nSLpK0pVBnVnAG5JWAHcBn+uobXDqWyS9LGkh8E4im3+5I/CF846PK9/9V18w0jl3eJLd5YWZPQUc\n3+rYXa3KUxNtGxy/qDtjdDD+mL4M6teHjdsiYynbQkVs3LqbQf196xvnXGJ8M3EXdfk58bn7kzf7\nzHnnXOI8obioiycMJ2arFDaGSmlo8N0cnXOJ8YTi4nzo7XELGXDld/0qxTmXGE8oLs7XJp8QV35x\nV9KH2ZxzvYQnFBdHEhNOGBp37CcP/ydF0TjnMoknFHeIX14xPq7867mbUxSJcy6TeEJxh5DE6CF9\n4449Vv1qiqJxzmUKTyiuTY9cWxVX/vYTvhiBc65jnlBcm0IhMbisIO7Yn+e8nqJonHOZwBOKa9ef\nv3FuXPkbv1+Yokicc5nAE4prVygUoqIwfgeDGf9akaJonHPpzhOK69Cs6RfElW/500spisQ5l+48\nobgOhcNhBufG7/78rUc9qTjnDuUJxXXqye98KK78x+dW0NhkKYrGOZeuPKG4ToXDIUbn1cUd+8jP\nnktRNM65dOUJxSXkD9+dEld+bdVmttXUtVPbOXc08oTiEiKJswfGH/vUnf9NTTDOubTkCcUl7Cdf\n/WBcefWGHcxauDFF0Tjn0o0nFJcwSXxmQr+4Yz98fCFNPkDvnKMHEoqk8yQtlbRM0nXt1Lld0nJJ\nCyWN66ytpFslLQnqPyapT7Lfh4v4zIfPpsxqo+Udu/fx6XvnpzAi51y6SGpCkRQC7gDOBcYCUySN\naVVnEnCMmR0LXAXcmUDb2cBYMxsHLAe+lsz34eJ9+7Iz48oLXl3Dyi17UxSNcy5dJPsKZTyw3MxW\nm1kDMAOY3KrOZOBBADN7HiiRVNFRWzP7m5k1Be3nAENxPeatbx5NZdP2uGPTHluEmXd9OXc0S3ZC\nGQKsjSmvC44lUieRtgCfBP56xJG6w/Krm6aQZY3R8svL1nPVfQtSGJFzLtXSccNwJVxR+jrQYGYP\ntVdn2rRp0edVVVVUVVUdSWwuMKBvMZW2g9fVP3ps/ZbdrN2+j2HlBR20dM6lm+rqaqqrq4/4PMlO\nKOuB4THlocGx1nWGtVEnp6O2kj4BvAd4R0cBxCYU170eue1KJl97L+tCkd0d12/ZxfQ/LeZXnzoN\nKeG/C5xzKdb6j+3p06d36TzJ7vKaB4yWVCkpB7gEmNmqzkzgMgBJE4BdZra5o7aSzgO+ArzPzHy6\ndoqEwyHMM+rfAAAVfklEQVQ+eu44oGXsZP7iNXz6Xu/6cu5olNSEYmaNwFQid2UtBmaY2RJJV0m6\nMqgzC3hD0grgLuBzHbUNTv0zoAh4RtILkn6RzPfh2jflPadzTNO2uGN79u5n7sodKYrIOZcq6s13\n5kiyTHx/E7/2ODsPRAa87/3sWZx63MBOWqTWrpp9XPaN37ImVB49dtrY4fziE6eSk+VzZ53LNJIw\ns8Put/Z/7e6IlRYXMHpwGflWHz02f/EaPvfrF1IYlXOup3lCcd3itus+xGDbHXds9979fOm3vg+9\nc0cLTyiu2/z8xo8wqmlrtLx89Rb27G9gwRs7UxiVc66neEJx3WZgvz6MHtafwU27oscWvLqGX/79\ndfYeONhBS+dcb+AJxXWrW//fheTTQI61JJBV67fxxd8u9KVZnOvlPKG4bvfgLZczzFq6ubbtqqWu\nvsHnpzjXy3lCcd2uMD+Xj7//LXHjKa8s34CZccU9vtS9c72VJxSXFO+beDICRsRMelzw6hoAfv2v\nVakJyjmXVJ5QXNI8+pOrCGMMihmkf+m1dfxn2Tb+t3x7By2dc5nIE4pLGkk88L3LKaCBEtsHQMPB\nRrbsqOHeZ9/wTbmc62U8obikKirI5borzqOf1RIK9kRbs3EH++vq+e7MpWzZcyDFETrnuosnFJd0\n408cwZuOHcxIa+nmWrxiI42NTdzwyCJ21tZ30No5lyk8obgeMX3q+wA4JubOrxeXrsXM+MrDL7N7\nX0OqQnPOdRNPKK7HPPbTzwDE3U4cufPL+PJDL/mVinMZzhOK61GP/uQqRHxSmb84klS+8vDLPqbi\nXAbzhOJ6lCQe+sGn2k0qNzyyiNc3+91fzmUiTyiux+XmZHP/dz7eblL53pNL+fdrW9tt75xLT55Q\nXEr0Kcrnzps+iogfqI8kFXjg36u545kVKYrOOdcVnlBcyvTvW8wd35gCtE4qqzEzFq7e5Wt/OZdB\nkp5QJJ0naamkZZKua6fO7ZKWS1ooaVxnbSVdJGmRpEZJb072e3DJM6h/CT+/8SNAJKmIyBL3C15d\nQ1MwEfKKe+b70vfOZYCkJhRJIeAO4FxgLDBF0phWdSYBx5jZscBVwJ0JtH0F+ADwbDLjdz1jYL8+\n/OpbHwNgVNO26DItL7y6lvqGyL4qn753Adtq6lIWo3Ouc8m+QhkPLDez1WbWAMwAJreqMxl4EMDM\nngdKJFV01NbMXjOz5YCSHL/rIX1LCvnNLZ8EoJ/VRnd9fHnZenbuqQXg+t+/wm+eW52yGJ1zHUt2\nQhkCrI0prwuOJVInkbauFynIz+H3P/o0APk0MDJY+v71tdtYvGIDAM8u2epdYM6lqaxUB9CGbr3q\nmDZtWvR5VVUVVVVV3Xl6182yssI8+pOruOiLdxHCGNW0lZWh/uyva2D+4tWcNnY4ID597wK+Mfn/\nGNG/MNUhO5fxqqurqa6uPuLzJDuhrAeGx5SHBsda1xnWRp2cBNp2KjahuMwgicd++hkuvObO6G3F\nW1RMjfKYv3gNJx43hNzsLG5+YgkA91xxWmoDdi7Dtf5je/r06V06T7K7vOYBoyVVSsoBLgFmtqoz\nE7gMQNIEYJeZbU6wLfg4Sq/12E8/wyfefyYAA6yGyqbIasWvLFvPa29sita74p75rNpam5IYnXMt\nkppQzKwRmArMBhYDM8xsiaSrJF0Z1JkFvCFpBXAX8LmO2gJIer+ktcAE4M+S/prM9+FS54KJJ3HP\nty8DIIum6HyVmn110fkqADc/scTHVpxLMfXmf4CSLBPf38SvPc7OA40A3PvZszj1uIEpjij1zIyL\nvnhXtLyfLDaEygAoLy1k5JB+0dfOOq6cy98+ssdjdK63kISZHXbvj8+UdxmheVxlynvHA5DPweg6\nYNt31TJ/8WoONkaS8HPLtnPFPfN9kUnnepgnFJdRLnr3m5nxw8itxc0D9sODsZWFS9cxf3HLPJXv\nPbmUK+6Zz579vnmXcz3BE4rLONnZYR776Wd491knRMrB2EqxRfZSmb94Nas3tGw3fO3vXuKKe+az\nv74xJfE6d7TwhOIy1lUXv51HbrsyWh5gNdFusK079zJ/8Wp27G65++vqB1/0KxbnksgTisto4XCI\nx376Gb5zzfuBlm6w5sSyct025i9eza6afdE2zVcsG3buT0XIzvVanlBcrzBm1EAe++lneMu4Y4CW\nxNK8fMuKNVsPuWL55mOLueKe+b6Zl3PdxG8bTkN+2/CRu/CaO+PKTYg3Qi23Fg+tKGNgvz5xdYaX\nF3DtpOMoykvHFYmc6zldvW3YE0oa8oTSPVrPXQEwYKNK2K8cAPJzsxkzciDhcPzF+gdPG8Kkkwci\n+UIM7ujjCaUNnlBcsytufJCde1rGUQzYTT7bQ0XRY5WD+9K/rIjWq/lcOXEUp48q8+TijhqeUNrg\nCcW19vc5S/jFw/H7stUTZl2oDItJJMePqKC4MO+Q9h87q5K3j+nnycX1ap5Q2uAJxbVnw5ZdfPGW\nR2hsbIoea+uqBeDYygGUFOUfco7xo/pyyVuG0Sc/O9nhOtejPKG0wROK64yZ8fun5vOHpxbEHW8C\ntgVL5sca3L+Egf36EAodeoPkh8YPZeIJA8jJ8psnXWbzhNIGTyjucOzdV8cP7nuaRcs3xB2PJJci\nahR/lZIVDjF8UF/K+hS02QX20TOHc9qoMorz/ArGZRZPKG3whOK6aueeffz4gb9Ftx5uZsAe8tgW\nKj6kTX5uNgP79aG0TwHhNq5gxo/qy1nHlXPswGK/inFpzRNKGzyhuO5woK6Bh/8yjz8/+/IhrzUQ\nYruKqFVum237lhRQXlJEcWFum91kbxrah9NH9WXM4GLKi9o+h3M9zRNKGzyhuGRYvnozv/rDf3h9\n7aEz7OsJs0sF7FVu3F1jsYrycyjtU0Cfwjzy83IO6S7LDotxlaWMGdSH0RVFVJTkkhX2KxrXczyh\ntMETiks2M+O1NzbzzP+WUD33tUNeb0TsI4ca5UUnU7anMC+HooJcCgtyyc/LJi8n+5BkU1aYzcj+\nhYzsX8jQvgUMKs2jrDCHcMhvY3bdp6sJxdeYcO4ISGLMqIGMGTWQqz86EYCa2gPMe2UVz85fxqLl\nGyimjmKriwzAEEky+8lhr3LjuspqD9RTe6AedtQc8n2ys8Lk52ZTkJfD8nVZ5OZmk5udRXZWOC7p\nFOdl0b9PLgNL8hhUmseAPnn075NLSX42xXlZhDzxuCRKekKRdB7wEyILUd5rZt9vo87twCSgFviE\nmS3sqK2kMuD3QCWwCrjYzHYn+704l4jiwjzeMWEM75gwJnqsdn8dS1ZuYs5LK5m/aDXh2gMUxSQZ\nAxoIs59s6pRNHVnUq+WfZ8PBRhoONrKn9kC73zcnSC7Z2WEK8nLIyQ4TDoXIyc6KPA+HyMoKEVKI\nrJAYWp5PVihEaUE2w8oLAOhXlENJQTb5OWGK87IpzA2TkxXyiZwuIUlNKJJCwB3AOcAGYJ6kJ8xs\naUydScAxZnaspDOAO4EJnbS9Hvibmd0q6Trga8GxXmXv2kXAWakOo8uqq6upqqpKdRhd0t2xF+bn\nctrYSk4bWxl3vHZ/HavWb2fZqs0sXbmJ11ZtpqY2uEIJkk0TUE8W9WRRp6xosmk9RlN/MNJNWtdw\nkE2vLaBo2JvajSccEnOajIK8HPbX1VNaXMCBugb6FOXR0NBIQX4uZhZNSggKcrM52GSUF+VSkBum\nICeLYf0K2FHbwOiKIvbsb2BIWX70DrbSghwkKMgJk5sdJjss8rLDZIdDZIdFOKR2E1Um/78DmR9/\nVyX7CmU8sNzMVgNImgFMBpbG1JkMPAhgZs9LKpFUAYzsoO1k4Oyg/QNANb0xoaxbnOoQjkgm/6Pq\nqdgL83MZO3owY0cPPuS1+oaDbN5ew/rNO1m7aSer1m9n3aadbNq+h4MHW3afbAIOEqah+aEw29a9\nQsnQEzAJg0OST2NTJFvtO1APEF3nbH9dZPOxHTHrnnVGguahytzsLCQ4UH+QovxcFIq8Vl9/kKLC\nXCQRkth3oJ7igjwkyM0OYU3G/oYmBgY3ICz48wMcu0D0LwxRlB8ZI9qy9yAjyvPIDofICoeoP9iE\nIfoX55AVDpEVFlnhEDV1jfQvirRprpsVDnGwycgPkltIamkTCpGVJZoMcrPChEIiJAgFsSp4rugx\ngjqRYyJ4PQQi8vo///nPjP1//0gkO6EMAdbGlNcRSTKd1RnSSdsKM9sMYGabJA3ozqCdSwc52VkM\nG1jGsIFlTDi57ToHDzayY88+9tTsZ8vOGjZu3c3WHTU8vrqAUyqz2LBlF6XFBazbvBMDGglxkBCN\nwaNB4aC7LYsGQoQxDiibLGvkoMIJxRl730tdw8Ho87376+Lq7dgdn6Rq99cfcq4twfjR5p21aN02\nVrR6/YWEIjpyiv6n+UskeURfjykcbGwiOxwGtSwrumv+Cj62YSejB5f1SLzpIh0H5bvSWZt5t3I5\n1w2yssIM6FvMgL7FjK5s+btq05J/Mu1LHzikvplRV3+QPbUH2H+ggZ17ajnY2MTGLbvJzgqzct1W\nSosLWPrGJspKCti4ZTc1++roU1zIq6u2UNKnkIMGO2sOQChMvYmQRZJQNo3UE6aJEGGaOEA2IZoI\nAXXBeFDYmmhU+t8CbdH/NH+xVr9l4n/lNDQ2xpX37G/gwb8t4VuXnZm0GNOSmSXtAUwAnoopXw9c\n16rOncCHY8pLgYqO2gJLiFylAAwElrTz/c0f/vCHP/xx+I+u/M5P9hXKPGC0pEpgI3AJMKVVnZnA\n54HfS5oA7DKzzZK2ddB2JvAJ4PvAx4En2vrmXbmP2jnnXNckNaGYWaOkqcBsWm79XSLpqsjLdreZ\nzZL0HkkriNw2fHlHbYNTfx94RNIngdXAxcl8H8455zrXq2fKO+ec6znpPzp2GCSVSZot6TVJT0sq\naafeKkkvSXpR0tyejrNVLOdJWippWTCnpq06t0taLmmhpHE9HWNHOotf0tmSdkl6IXh8IxVxtkfS\nvZI2Szp05ceWOmn5+XcWewZ89kMl/UPSYkmvSPpCO/XS9fPvNP50/RlIypX0fPA78BVJN7VT7/A+\n+2QOyvf0g0hX2FeD59cBt7RTbyVQlgbxhoAVRGb8ZwMLgTGt6kwC/hI8PwOYk+q4DzP+s4GZqY61\ng/fwVmAc8HI7r6fz599Z7On+2Q8ExgXPi4DXMuz//0TiT9ufAVAQfA0Dc4DxR/rZ96orFCITHh8I\nnj8AvL+deiI9rs6iEz/NrAFonrwZK27iJ9A88TMdJBI/dO1W8B5hZv8BdnZQJW0//wRih/T+7DdZ\nsMySme0lcvfmkFbV0vnzTyR+SNOfgZk1TwzKJTKe3nr847A/+3T4pdqdBljMhEegvQmPBjwjaZ6k\nT/dYdIdqb1JnR3XWt1EnVRKJH+AtwSXzXySd0DOhdZt0/vwTkRGfvaQRRK62nm/1UkZ8/h3ED2n6\nM5AUkvQisAl4xszmtapy2J99Ok5s7JCkZ4jMU4keIpIg2uqbbO+Og7PMbKOk/kQSy5Lgrz3X/RYA\nw81sX7Bu2+PAcSmO6WiREZ+9pCLgUeCa4C/9jNJJ/Gn7MzCzJuAUSX2AxyWdYGavHsk5M+4Kxcze\nZWYnxTxODL7OBDY3X5JJGghsaeccG4OvW4E/cehyMD1lPTA8pjw0ONa6zrBO6qRKp/Gb2d7mS2sz\n+yuQLalvz4V4xNL58+9QJnz2krKI/DL+jZm1NZ8srT//zuLPhJ+Bme0B/gmc1+qlw/7sMy6hdKJ5\nwiO0M+FRUkHwFwWSCoF3A4t6KsBWohM/JeUQmbw5s1WdmcBlALETP3s2zHZ1Gn9sn6uk8URuVd/R\ns2F2SrTfz53Onz90EHuGfPb3Aa+a2U/beT3dP/8O40/Xn4Gkfs13wUrKB95F/KK90IXPPuO6vDrR\n5oRHSYOAX5nZ+US6y/4kyYi8/9+Z2exUBGtHMPEzHSQSP3CRpM8CDcB+4MOpi/hQkh4CqoBySWuA\nm4AcMuDz7yx20v+zPwv4KPBK0JdvwA1E7hrMhM+/0/hJ35/BIOABRbYJCQG/Dz7rI/rd4xMbnXPO\ndYve1uXlnHMuRTyhOOec6xaeUJxzznULTyjOOee6hScU55xz3cITinPOuW7hCcX1OpIGSPqdpBXB\nem3PSWpr0cq0JunkYLmO5vIFkr4aPL9J0rVJ/v41yTy/6308obje6HGg2sxGm9npRGbwD01xTF0x\nDnhPc8HMnjSzW3vw+/skNXdYPKG4XkXSO4A6M/tV8zEzW2tmPw9er5T0L0nzg8eE4PjZkqolPR5c\n2XxP0keCTYhekjQyqNdP0qPB8eclvSWm/YuKbKK0IFjWJzauSkmvxJS/LOmbwfN/SrolON9SSWdJ\nyga+BVwcnPNDkj4u6WedvP9Rkv4XxPzt2KsMST9QZDOllyQ1ryJRKOlvwWfxkqT3HdEPwB3VetvS\nK86NBV7o4PXNwDvNrF7SaOBh4PTgtZOAMcAuIpuw/crMzlBkJ76rgWuBnwK3mdl/JQ0DngZOAL4M\nfM7M/iepADjQxvfu6C/+cPC9JgHTzOxdQcI51cy+ACDp452cgyC+H5vZI83LaARtLwROMrMTJQ0A\n5kl6FtgGvN/M9koqJ7LRUuv15JxLiF+huF5N0h2K7EXRvE9FDnCPItvm/gH4v5jq88xsi5nVA68T\nWaMM4BVgRPD8ncAdwdpNM4GiIIE8B/xY0tVEdgNtOsxQ/xh8XUBkLaiueguR1W8BHoo5fhaR5ImZ\nbQGqiSRSAbdIegn4GzA4SDjOHTa/QnG9zWLgwuaCmU0N/vJu3jzoS8AmMztJUpjIgn3N6mKeN8WU\nm2j5tyLgjGCHyljfl/Rn4L3Ac5LebWbLYl4/SGSr1WZ5rdo3f69GjuzfZewVTEc7BTa/9lGgHDjF\nzJokvdFGbM4lxK9QXK9iZv8AcoPunmax4xklwMbg+WXE/5JPxGzgmuaCpJODr6PMbHEwaD6PSNdZ\nrM1Af0llknKB8zv4Hs2/7GuAPocZ3xzgouD5JTHH/w18WJFd+voDbwPmEvk8tgTJZCLxV0dpuXWt\nS1+eUFxv9H6gStLrkuYA9wNfDV77BfCJoMvqOCLLcrelvbGKa4DTggHsRUBz4vpiMOC9EKgH/hp3\nMrODRAbZ5xEZd1nSwfdqLv8TOKF5UL79txvnS8C1QRzHALuD7/8n4GWguWvrK0HX1++A04Mur0s7\nicu5Dvny9c71IpLyzWx/8PzDwCVm9oEUh+WOEj6G4lzvcqqkO4h0V+0EPpnieNxRxK9QnHPOdQsf\nQ3HOOdctPKE455zrFp5QnHPOdQtPKM4557qFJxTnnHPdwhOKc865bvH/AbLsGV1f+aSfAAAAAElF\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f009786ee10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_dist1 = MakeGoalTimePmf(suite1)    \n",
    "time_dist2 = MakeGoalTimePmf(suite2)\n",
    " \n",
    "thinkplot.PrePlot(num=2)\n",
    "thinkplot.Pmf(time_dist1)\n",
    "thinkplot.Pmf(time_dist2)    \n",
    "thinkplot.Config(xlabel='Games until goal',\n",
    "                   ylabel='Probability')\n",
    "\n",
    "time_dist1.Mean(), time_dist2.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In overtime the first team to score wins, so the probability of winning is the probability of generating a smaller value of `t`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p_win_in_overtime 0.524145104619\n"
     ]
    }
   ],
   "source": [
    "p_win_in_overtime = time_dist1.ProbLess(time_dist2)\n",
    "p_adjust = time_dist1.ProbEqual(time_dist2)\n",
    "p_win_in_overtime += p_adjust / 2\n",
    "print('p_win_in_overtime', p_win_in_overtime)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can compute the overall chance that the Bruins win, either in regulation or overtime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p_win_overall 0.548000681433\n"
     ]
    }
   ],
   "source": [
    "p_win_overall = p_win + p_tie * p_win_in_overtime\n",
    "print('p_win_overall', p_win_overall)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** To make the model of overtime more correct, we could update both suites with 0 goals in one game, before computing the predictive distribution of `t`.  Make this change and see what effect it has on the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** In the final match of the 2014 FIFA World Cup, Germany defeated Argentina 1-0. What is the probability that Germany had the better team?  What is the probability that Germany would win a rematch?\n",
    "\n",
    "For a prior distribution on the goal-scoring rate for each team, use a gamma distribution with parameter 1.3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3103599490022571"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ujs2mOnv2LM/OXcE3f/gMazaV+VyhSNsRqGRVjz69mBm3TbqMnzzwCS4ZWNe7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f00973ff150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from thinkbayes2 import MakeGammaPmf\n",
    "\n",
    "xs = np.linspace(0, 8, 101)\n",
    "pmf = MakeGammaPmf(xs, 1.3)\n",
    "thinkplot.Pdf(pmf)\n",
    "thinkplot.Config(xlabel='Goals per game')\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** In the 2014 FIFA World Cup, Germany played Brazil in a semifinal match. Germany scored after 11 minutes and again at the 23 minute mark. At that point in the match, how many goals would you expect Germany to score after 90 minutes? What was the probability that they would score 5 more goals (as, in fact, they did)?\n",
    "\n",
    "Note: for this one you will need a new suite that provides a Likelihood function that takes as data the time between goals, rather than the number of goals in a game. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "**Exercise:** Which is a better way to break a tie: overtime or penalty shots?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "**Exercise:** Suppose that you are an ecologist sampling the insect population in a new environment. You deploy 100 traps in a test area and come back the next day to check on them. You find that 37 traps have been triggered, trapping an insect inside. Once a trap triggers, it cannot trap another insect until it has been reset.\n",
    "If you reset the traps and come back in two days, how many traps do you expect to find triggered? Compute a posterior predictive distribution for the number of traps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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